q-TASEP with position-dependent slowing

We introduce a new interacting particle system on Z, slowed t-TASEP. It may be viewed as q-TASEP with additional position-dependent slowing of jump rates, depending parameter t, which leads to discrete asymptotic fluctuations at large time. If the other hand t→1 time→∞, we prove A law numbers for positions, central limit theorem, convergence fixed-time Gaussian marginal stationary solution SDEs derived from and bulk certain explicit process R, scaling exponents characteristic Edwards-Wilkinson universality class in (1+1) dimensions. The proofs relate t-TASEP Hall-Littlewood process, use contour integral formulas observables this process. Unlike most previously studied Macdonald processes, one involves only local interactions, resulting asymptotics (1+1)-dimensional rather than (2+1)-dimensional systems.